Geometric object with magnitude (length) and direction.

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0
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2answers
134 views

Mathematically determining the direction of torque?

I need to mathematically derive the direction of torque in a 2D plane(clockwise/anticlockwise), for a physics engine. I have torque calculated, but it is always positive, so rotation always is in the ...
2
votes
1answer
439 views

The curl of a special cross product

When given two vectors $\mathbf{A}$ and $\mathbf{B}$, the curl of the cross product of these two is given by ...
1
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2answers
275 views

Need clearing up on vector decomposition in motion physics

I've been pursuing physics on my own, and I need something cleared up. Say I have two arbitrary objects, I have their velocities, I know when the collide, I have their normal vectors, etc. I know ...
0
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0answers
51 views

Vector Equilibrium

I'm trying to understand more about this 'vector equilibrium' apparently coined by R.Buckminster Fuller. In this site (http://cosmometry.net/), it claims: "The Vector Equilibrium, as its name ...
5
votes
2answers
597 views

Understanding the difference between co- and contra-variant vectors

I am looking at the 4-vector treatment of special relativity, but I have had no formal training in Tensor algebra and thus am having difficulty understanding some of the concepts which appear. One ...
8
votes
5answers
9k views

Why is current a scalar quantity?

Current has both magnitude and direction. As per the definition of vector defined in encyclopedia, current should be a vector quantity. But, we know that current is a scalar quantity. What is the ...
0
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1answer
218 views

What is this vector problem asking to find, the magnitude of the force F or the component of it that goes along the ramp?

A shopper pushes a 7.5-kg shopping cart up a 13 (degree)incline. Find the magnitude of the horizontal force, F, needed to give the cart an acceleration of 1.41 m/s$^2$. I ask this because the ...
2
votes
1answer
95 views

$\hat{\imath}$ component of force exerted on an electron by a magnetic field?

The magnetic field over a certain range is given by $\vec{B} = B_x\hat{\imath} + B_y\hat{\jmath}$, where $B_x= 4\: \mathrm{T}$ and $B_y= 2\: \mathrm{T}$. An electron moves into the field with a ...
0
votes
2answers
116 views

Stellar Power(Luminosity) Flux

So I was applying some mathematical techniques I learned to physics, and one thing that captured my interest, is the power or luminosity flux of a star. So modeling the situation, taking the scalar ...
-2
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3answers
211 views

Velocity of the photon

As far as I know photon travels in a wave pattern, that means it has $x$ and $y$ axis velocity components. If photon travels along $x$ axis, then what is it's maximum $y$ axis velocity?
6
votes
4answers
500 views

Is the covariance or contravariance of vectors/tensors something that can be “visualized”?

I'm taking an undergrad GR course, and our text (Lambourne) mentions covariant and contravariant vectors and tensors ad-nauseum, but never really gives a formal definition for what they are, and how ...
0
votes
2answers
144 views

Relative velocity of boat

I am trying to understand fully the following question: A boat is traveling west at 100m/s and is partially helped by a strong wind blowing at 20m/s 30 degrees north of west. What speed could the ...
1
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1answer
152 views

Understanding vectors in physics: notation

We have the formula for the Lorentz force $$\textbf{F} = q \space(\textbf{E} + \textbf{v} \times \textbf {B})$$ This is a simple formula you learn in high school, but I'm interested to self-study ...
7
votes
2answers
310 views

Can we show that time is orthogonal to space?

It's easy to show that the time we measure is "in a different direction" from the space directions we measure. However, it's not immediately obvious to me that these directions are orthogonal. How do ...
0
votes
1answer
246 views

Vector Maths to Simulate Car Physics [closed]

I'm working on a 3D program that involves controlling a Cube on-screen (which represents a car). I use C++, OpenGL and GLM (for vector and matrices etc, if you're familiar with programming; Once the ...
1
vote
2answers
329 views

Angular position vector?

I'm a mathematician, so I like my angular velocities to be vectors. It makes my angular momenta and torques vectors as well, and so they have nice operations I can do on them. Because of that, I pick ...
0
votes
0answers
58 views

How to interpret the factor $\frac{(\vec v\cdot \hat n)}{|\vec v| 4\pi r}$?

There is a small area element of size $da$ and normal vector $\hat n$. I understand that the particles with speed $|\vec v|$ that hit this area element in the time interval $(t,t+\delta t)$ lie in a ...
2
votes
3answers
9k views

Vertical and horizontal components of forces and vectors

I'm getting a bit confused when finding components of vectors and forces. In problems for vectors, I've always known that if you want to get the components of a vector, you would use the following: ...
2
votes
2answers
972 views

I don't understand the idea of perpendicular vectors being independent of each other?

So problem 71-75 is about vectors. The problem says: A river has a current flowing with a velocity of 2.0 meters per second due east. A boat is 75 meters from the north riverbank. It travels at ...
-3
votes
1answer
108 views

Vector analysis query [closed]

I cannot understand how and why those two expressions are coming (the ones I have highlighted). Please explain.
0
votes
3answers
811 views

Basic vector addition problem [closed]

This is the entire problem: A student adds two vectors with magnitudes of 200 and 40. Taking into account significant figures, which is the only possible choice for the magnitude of the resultant? ...
2
votes
3answers
15k views

Why work is a scalar and not a vector?

Work (in physics) is a scalar but why? and why not a vector?
1
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2answers
1k views

How to find the resultant of two forces? [closed]

I got this question in a assignment and haven't been able to figure out how to get to the correct result. A force of 6 newtons and a force of 10 newtons can be combine to form a resultant of ...
3
votes
2answers
4k views

Resultant of two forces acting in the same line

I'm quoting the definition of Resultant of two forces acting in the same line from the book "A FIRST COURSE IN PHYSICS" one of whose authors is Robert Andrews Millikan: The resultant of two forces ...
0
votes
1answer
90 views

Vector Summation [closed]

When two vectors are sketched from a single point, the angle between them is θ. Show that the size of their vector summation is given in the expression: $ \sqrt{A^2 + B^2 +2ABcosθ} $. Any ...
-1
votes
2answers
146 views

Vectors question? [closed]

I am stuck on this vectors question I have for home work. Does anything think they can help point me in the right direction on how to solve this? An explorer is caught in a whiteout (in which the ...
7
votes
3answers
740 views

Covariant and contravariant vectors

Reading Weinberg's Gravitation and Cosmology, I came across the sentence (p.115, above equation (4.11.8)) The partial derivative operator $\partial/\partial x^\mu$ is a covariant vector, or in ...
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vote
2answers
341 views

Angle needed for object A to intercept with object B

Object B is 15 degrees East of North at a distance of 20km/h. Object B is moving at an average speed of 30km/h in the direction 40 degrees East of North. If object A is capable of moving at 100km/h, ...
2
votes
2answers
5k views

Derive vector gradient in spherical coordinates from first principles

Trying to understand where the $\frac{1}{r sin(\theta)}$ and $1/r$ bits come in the definition of gradient. I've derived the spherical unit vectors but now I don't understand how to transform ...
2
votes
2answers
193 views

How to determine which one would not be the resultant?

i had a physics exam yesterday, which was all in all pretty good except for this one question which i just don't get.: ...
1
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0answers
103 views

Understanding unit vectors

Trying to understand how the unit vector ${\mathcal{\hat{r}}}$ defined as $\frac{r' - r}{|r' - r|} $ (where $r'$ is the source point) works in this problem: Work out the electric field, $E$, at point ...
1
vote
1answer
110 views

Commutation of abstract $O(3)$ generators and vectors [closed]

I've been given the following problem, and I'm quite lost with it. Let $L_1$, $L_2$, and $L_3$ denote the abstract $o(3)$ algebras. You are given that $\vec{A} = (A_1, A_2, A_3)$ and $\vec{B} = ...
0
votes
1answer
75 views

Vector Isolation/ Rotation

I have a series of vectors (current speeds) based on an ENU (East North Up) system. I would like to estimate the current speed of the water headed in a specific direction. In this example I am ...
2
votes
1answer
213 views

Equivalent definitions of vectors

Equivalent definitions of vectors. In maths a vector is an object that obeys some axioms of a vector space. But in physics a vector can be thought as an object which is invariant under rotations of ...
2
votes
2answers
347 views

About vector form of friction

I read a text on mechanics and in the chapter on friction, there written that the kinetic friction is in the form $$f_k = \mu_k F_N$$ where $f_k$ is the kinetic friction, $\mu_k$ is the kinetic ...
2
votes
1answer
4k views

How do I split a vector into components parallel and perpendicular to a known line?

Given $\mathbf{F}=\langle 7.20,−12.0,28.2\rangle\text{ Newtons}$, find the component of $\mathbf{F}$ that acts perpendicular to member DA such that the vector addition of the perpendicular and ...
2
votes
2answers
461 views

Why do smaller objects become harder to break?

When grabbing a typical tree branch of at least two feet, it's so easy to snap with a less than one inch circumference that even a toddler can do it. However, after breaking it, the smaller halves ...
0
votes
1answer
331 views

Rotating point in 3D space by Unknown rotation vector [closed]

I have a random point defined by: int x = rand.nextInt(9)-4;//-4 to +4 int y = rand.nextInt(4)+2;//+2 to +5 int z = rand.nextInt(9)-4;//-4 to +4 Y happens to be ...
1
vote
1answer
232 views

Spinor formalism in QFT

We can describe fields by two formalisms: vector and spinor. This is the result of possibility of representation of the Lorentz's group irreducible rep as straight cross product of two $SU(2)$ or two ...
0
votes
1answer
2k views

Find angle of force vector in equilibrium

So my question is Rope BCA passes through a pulley at point C and supports a crate at point A. Rope segment CD supports the pulley and is attached to an eye anchor embedded in a wall. Rope segment ...
3
votes
2answers
1k views

Finding force vectors

A tugboat tows a ship at a constant velocity. The tow harness consists of a single tow cable attached to the tugboat at point $A$ that splits at point $B$ and attaches to the ship at points $C$ and ...
0
votes
1answer
243 views

Why Counterclockwise starts from East?

In vector lessons, we have counterclockwise angle of rotation of the vector starts from East. "The direction of a vector is often expressed as a counterclockwise angle of rotation of the vector about ...
0
votes
1answer
71 views

Asking the vector form of the equation about velocity

In the undergraduate text of physics, the equation for velocity and displacement at constant acceleration are given in scalar form. For example, my text reads $$v^2 = v_0^2 + 2a(x-x_0)$$ But today, ...
3
votes
3answers
674 views

How do I meaningfully divide by a vector?

How long does it take a baseball with velocity $(30, 20, 25) m/s$ to travel from location $r_1 = (3, 7,−9) m$ to location $r_2 = (18, 17, 3.5)m$? I am thinking that it should be the ...
0
votes
1answer
97 views

Combine forces (gravity)

I have a point at which there are (at least) two different forces (gravity to be precise) working. How do I combine those so that the force acting on the point are as realistic as possible? To put ...
2
votes
5answers
224 views

How does this shell hit the aircraft?

A fighter aircraft is flying horizontally at an altitude of 1500m with speed of 200m/s. The aircraft passes directly overhead an anti-aircraft gun. The muzzle speed of the gun is 600m/s. ...
0
votes
2answers
449 views

Why do we say that in Coulomb's law the force is proportional to $\frac{1}{r^{2}}$ and not $\frac{1}{r^{3}}$?

I am going over Coulomb's law and there is something that is a bit confusing for me: According to Coulomb's law, if I have a charge $q_{1}$ at a point $\vec{r_{1}}$ and a charge $q_{2}$ at a point ...
0
votes
1answer
195 views

Equations of circular motion

I have studied that a finite angular displacement $\triangle \theta$ is a scalar. But, $\delta \vec \theta$ is a vector. Now, when it is a uniformly accelerated motion we are dealing with, we use ...
1
vote
1answer
131 views

Interchaning a position between two reference frames?

$\vec{r}_a$ is a positional vector from reference frame $a$. What is the position of same point from reference frame $b$ ? If required, assume position of origin of frame $a$ is $\vec{m}$ and ...
1
vote
4answers
620 views

Vectors with more than 3 components

I have some confusion over Vectors, Its components and dimensions. Does the number of vector components mean that a vector is in that many dimensions? For e.g. $A$ vector with 4 components has 4 ...